Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

11.4 Electron transfer reactions (Marcus theory) 236
(4) The ET rate constant is described by TST as
=
exp ¡ −∆ + ¢ (11.45)
The Gibbs free energy of activation
∆ + = 2 (11.46)
is the difference from the donor minimum to the TS at the donor/acceptor curve
crossing at point .
(5) In order to relate ∆ + to the potential curves, we define the “reorganization
energy” as the energy that the acceptor would have at the equilibrium
geometry of the donor. This is the energy of the acceptor parabola () at
=0.
If we count from the minimum of the acceptor parabola (), wehave
=(− ) 2 = 2 (11.47)
(6) We now determine the energy of the intersection point of the two parabolas
from the condition
( )= ( ) . (11.48)
Inserting into Eqs. 11.43 and 11.44 yields, and using Eq. 11.47, yields
2 =( − ) 2 + ∆ ª (11.49)
= 2 − 2 + 2 + ∆ ª (11.50)
= 2 − 2 + + ∆ ª (11.51)
y
y
y
y
2 = + ∆ ª (11.52)
∆ + = 2 = ( + ∆ ª ) 2
( )=
= + ∆ ª
2
(11.53)
= ( + ∆ ª ) 2
(11.54)
4
2 4
Ã
!
exp − ( + ∆ ª ) 2
(11.55)
4
(7) Limiting cases: We can distinguish between
• −∆ ª : Regular region – the reaction becomes faster, the more
exergonic the reaction becomes.
• −∆ ª = : turning point
• −∆ ª : Inverted region – the reaction becomes slower, the more
exergonic the reaction becomes.